How do we get from the simple definition of π as the ratio of a circle's perimeter to its diameter to the dance of its decimal digits? The answer depends on when the question is asked!
Any primary-school pupil who has drawn a rosette knows that a hexagon can be obtained simply by marking off a circle's radius R around its circumference. This simple observation may be what first sparked some people's love of geometry.
It follows that the perimeter is "a little greater" than six times the radius, giving an initial value for π—namely 3, with no decimal places.
At first, geometry
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